A hybrid electric vehicle powertrain typically includes an internal combustion engine and a transmission, with the transmission having one or more high-voltage electric traction motors. The engine and/or the electric traction motors may provide input torque depending on the commanded powertrain operating mode. In an electric vehicle (EV) drive mode in particular, the engine remains off. The electric fraction motor(s) in EV drive mode are powered via a power inverter module, a high-voltage battery, and associated power electronics. When the engine is running, each electric traction motor may be operated as a generator to quickly recharge the cells of the battery. The engine may be automatically cranked and restarted when engine torque is needed, e.g., to shift the transmission to an electrically variable transmission (EVT) drive mode.